These two hexagonal space groups P6_3mcm and P6_3mmc (193 and 194 in International Tables) have different extinction rules: For the former space group we have hh-2hl no condition and h-h0l with l = 2n; for the later we have hh-2hl with l=2n and h-h0l no condition. These are clearly written in the International Table A, p. 588-591. If you wish to derive these rules then just look at the structure factor expressions also given in International Tables vol 1 (old version, red) p. 488-489.

A "space group change via centering translation" understanding that you change from a primitive to a centered (face/s, body or R) cell will always reduce the number of observed peaks since integral systematic absences will apply to the new space group but not to the primitive one.

Now, I'm not sure of understanding your question since the two space groups you mention have no change in centering translation. The two space groups are related by a change in the direction used to modify the 6/mmm point group with the addition of a glide component along c to [100][010][-1,-1,0] (P63/mcm) or [1,-1,0][120][-2,-1,0] (P63/mmc) equivalent directions.

Could you please clarify your question?

Glide is also involves a traslation but is cobined with a rotation. Glide is definitely not a centering translation and therefore its extinction is different from that of centering. Leopoldo has already explained how the centered lattice have some extinct reflections. Magesh, read some text book on X-ray crystallography and refresh your knowledge about symmetry and extinction rules.

Thank you very much Tapan Chatterji for pointing out that the decrease of symmetry elements is not the only condition. its the actual wackyof positions that decides the extinction rule. I got carried by away by the symmetry arguments.

Thank you Leopoldo, What i mean centering translation is the additional Centering translation or loss of centering translation which converts phase domains into anti phase domains. one can be converted in to another by looking along the [1 2 0]. here the loss of centering happens to be at four of the eight corners of primitive lattice (converts six fold axis into 3-fold axis) thus can be considered as a primitive unit cell of enlarged size. here both the unit cell are primitive but the choice of the unit cell side changes form [1,0,0] to [1,2,0] with different lattice parameter. but i do not know how it is different from a face centered or body centered lattice (i guess in this case, a reduction in the number of symmetry elements)

You are looking at the centering in a complex. It is far simpler than that. If your cell is body-centered it simply means that for every atom at xyz you will have an atom at x+1/2, y=1/2, Z+1/2, so your translation is 1/2,1/2,1/2. The space group symbol will have I at the first place, meaning "innencertriert" or body centered. You will have reflections hkl only with h+k+l=2n. So you will have less number of reflections compared to the P cell of same size. Why? Because you chosen a cell which is not a primitive cell, the primitive cell is smaller than the cell you have chosen. The penalty for this is that you will have some extinct reflections h+k+l=2n+1. In the case of fcc cell your translations are 01/21/2, 1/21/20, 1/201/2. These translations are actually lattice translations because if have chosen a larger cell than the primitive rhombohedral cell. Again the penalty is that you will have extinction hkl either all odd or even. You will have reflections with mixed odd even indices like 120 for example.